Unit 6, Lesson 16

Finding Cone Dimensions

Accelerated 7

Practice

Problem 1

ForLesson 15: The Volume of a Cone

The volume of this cylinder is \(175\pi\) cubic units.

What is the volume of a cone that has the same base area and the same height? Explain how you know.

Problem 2

A cone has volume \(12\pi\) cubic inches. Its height is 4 inches. What is its radius? Explain how you know.

Problem 3

A cone has volume \(3 \pi\) cubic units.

If the cone’s radius is 1 unit, what is its height?
If the cone’s radius is 2 units, what is its height?
If the cone’s radius is 5 units, what is its height?
If the cone’s radius is \(\frac 1 2\) unit, what is its height?
If the cone's radius is \(r\) units, what is its height?

Problem 4

ForLesson 5: Even More Graphs of Functions

Three people are playing near the water.

Person A stands on the dock.

Person B starts at the top of a ladder, slides into the water, then climbs out of the water.

Person C climbs out of the water and up the slide ladder.

Coordinate plane, x, negative 1 to 8 by 1, y, negative 10 to 20 by 5. Three lines.

Match the people to the graphs on the coordinate plane where the horizontal axis represents time in seconds and the vertical axis represents height above the water level in feet.

Problem 5

ForLesson 3: Equations for Functions

A room's ceiling is 15 feet tall. An architect wants to include a window in the room that is 6 feet tall. The distance between the floor and the bottom of the window is \(b\) feet. The distance between the ceiling and the top of the window is \(a\) feet. This relationship can be described by the equation \(a = 15 - (b + 6)\).

Which variable is independent based on the equation given?
If the architect wants \(b\) to be 3 feet, what does this mean in the context of the room? What value of \(a\) would work with the given value for \(b\)?
The customer wants the window to have 5 feet of space above it. Is the customer describing \(a\) or \(b\)? What is the value of the other variable?

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